We propose a scheme for routing and placement of mobile data collectors in Underwater Acoustic Sensor Networks (UASNs). The proposed scheme maximizes the lifetime of the network with an upper bound on the maximum delay. We assume a 3D architecture, in which on-the-surface data collectors gather data from underwater sensors and relay them to an on-shore sink. We divide the lifetime of the network into fixed length rounds and move the data collectors to new locations at the beginning of each round. This problem is formulated as an Integer Linear Program (ILP), and we use an ILP solver to find the optimal placement of data collectors together with the multi-hop routing paths to deliver data from underwater sensors to data collectors. To the best of our knowledge, this is the first attempt towards the placement of data collectors in a 3D environment with delay constraints. When compared with other schemes, our scheme has shown the capability to achieve longer lifetime and shorter delay.